Order of acquisition, or?

In Fluent Forever the following passages raise the possibility of there being a single best order in which to learn the grammar of each given language:

if you monitor adults learning a second language, you find something completely mystifying. That German woman with her English textbook follows the exact same developmental stages as that Japanese guy with his American girlfriend. The German might progress through her stages faster— German, after all, is fairly similar to English— but she won’t skip any of them. [...]

while some learners can move through these stages more quickly than others, no amount of drilling a particular grammar rule— I eat, he eats, we sit, she sits, they fall, it falls— will enable a student to skip a developmental stage. Ever. Naturally, it’s not just English. While the developmental stages look different from language to language, every language has a particular developmental order, which children and second language learners alike will inevitably follow on their way to fluency. The most plausible explanation for these rigid, unavoidable developmental stages is this: our language machines never turn off. When we learn a second language, we develop like children because we learn like children.

It would be interesting to know more about the research being drawn on here, and where one might find evidence for the developmental pattern in specific languages.
Also, are we talking about "order of acquisition" here? A cursory web/Google Books search suggests order of acquisition is uncertain for second languages.